In many signal processing applications it is required to modify the sampling rate of a digitally-represented signal. Sampling rate conversion commonly involves the use of interpolation or decimation filters. An interpolation filter accepts a sequence of input samples having an input sampling rate and produces a sequence of output samples having a higher output sampling rate. The ratio between the output and input sampling rates is referred to as the interpolation factor. Similarly, a decimation filter accepts an input sequence and produces an output sequence having a lower output sampling rate. The ratio between the input and output sampling rates is referred to as the decimation factor.
Interpolation and decimation filters are described in a variety of publications, such as a book by Crochiere and Rabiner entitled “Multirate Digital Signal Processing,” Prentice-Hall, 1983, chapter 1, pages 1-11, which is incorporated herein by reference.
Interpolation and decimation filters are sometimes implemented using polyphase configurations, for allowing the filter cells to operate at a lower sampling rate and reduce the filter computational complexity. Polyphase implementations are described by Vaidyanathan in a book entitled “Multirate Systems and Filter Banks,” Prentice-Hall, 1993, section 4.3, pages 120-133, which is incorporated herein by reference.
Interpolation filters are sometimes implemented by connecting several interpolation stages in series, in order to achieve higher interpolation factors. This configuration is commonly referred to as a multistage filter. The total interpolation factor of a multistage interpolation filter is the product of interpolation factors of the individual stages. High decimation factors are also achieved in a similar fashion. Multistage interpolation and decimation filters are described in chapter 5, pages 193-250, of the book by Crochiere and Rabiner cited above. This technique is also described by Renfors and Saramaki in a paper entitled “Recursive Nth-Band Digital Filters—Part II: Design of Multistage Decimators and Interpolators,” IEEE Transactions on Circuits and Systems, volume CAS-34, number 1, January 1987, pages 40-51, which is incorporated herein by reference.
There is known to be a duality between interpolation filter design and decimation filter design. This property is described in the book by Crochiere and Rabiner cited above (see in particular Chapter 3.1.3, pages 68-70). The duality principle is also described by Classen and Mecklenbräuker in a paper entitled “On Stationary Linear Time-Varying Systems,” IEEE Transactions on Circuits and Systems, volume CAS-29, number 3, March 1982, pages 169-184, which is incorporated herein by reference.